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将桩周土体视为粘弹性介质,利用分数导数粘弹性模型描述土体的力学特性,在Novak平面应变假定的基础上,借助于势函数并考虑土体边界条件求得了分数导数微分算子描述的粘弹性土层水平位移的衰减函数以及分数导数粘弹性土层的刚度和阻尼系数。利用Winkler动力弹簧-阻尼器模型模拟桩-土之间的动力相互作用,并在此基础上利用初始参数法求解了分数导数粘弹性土层中桩-桩水平动力相互作用和群桩的水平振动问题。以数值算例的形式讨论了分数导数微分算子的阶数和土体的模型参数对分数导数微分算子描述的粘弹性土层水平位移的衰减函数和群桩的水平动力阻抗的影响。研究表明:分数导数微分算子的阶数对土层水平位移的衰减函数的影响与桩间距和荷载方向角有关;分数导数粘弹性土中群桩的动力阻抗可以退化到经典粘弹性和弹性情况;分数导数微分算子的阶数和土体模型参数对群桩水平动力阻抗有较大影响。
The soil surrounding the pile is regarded as a viscoelastic medium, and the mechanical properties of the soil are described by means of fractional derivative viscoelasticity. Based on the Novak plane strain assumption, the differential derivative differential operator is obtained by means of the potential function and the soil boundary conditions Describe the attenuation function of horizontal displacement of viscoelastic soil layer and the stiffness and damping coefficient of fractional derivative viscoelastic soil. The dynamic interaction between piles and soil was modeled by Winkler dynamic spring-damper model. On this basis, the initial parameter method was used to solve the horizontal pile-pile dynamic interaction and pile group horizontal vibration in fractional derivative viscoelastic soil problem. In the form of numerical examples, the order of fractional derivative differential operator and the influence of soil model parameters on the attenuation function of horizontal displacement of viscoelastic soil and the horizontal dynamic impedance of pile group described by fractional derivative differential operator are discussed. The results show that the influence of order of differential derivative differential operator on the attenuation function of soil horizontal displacement is related to pile spacing and load direction angle. The dynamic impedance of pile group in fractional derivative viscoelastic soil can degenerate to classical viscoelasticity and elasticity The orders of differential derivative differential operator and soil model parameters have great influence on the horizontal dynamic impedance of pile groups.